Table 2.

Common methods to estimate the S–N curves²⁴.

Model	S–N curves relation
Basquin (1910)	$logN=A-Blog(\mathrm{\Delta }\sigma );\mathrm{\Delta }\sigma \ge \mathrm{\Delta }{\sigma }_{\infty }$
Stromeyer (1914)	$logN=A-Blog(\mathrm{\Delta }\sigma -\mathrm{\Delta }{\sigma }_{\infty })$
Palmgren (1924)	$\mathrm{\Delta }\sigma =b(N+B{)}^{-a}+\mathrm{\Delta }{\sigma }_{\infty })$
Bastenaire (1972)	$N=\frac{A}{\mathrm{\Delta }\sigma -E}\exp \left[-,C,\left(\mathrm{\Delta },\sigma ,-,E\right)\right]-B$
Ling and Pan (1997)	$F={\sum }_{i=1}^n\left\{\mathrm{In},(\sigma \left(S_i\right)),+,\frac{[log{N}_i-\mu (S_i{)]}^2}{2{\sigma }^2(S_i)}\right\}$
Kohout and Vechet (2001)	$log\left(\frac{\mathrm{\Delta }\sigma }{\mathrm{\Delta }{\sigma }_{\infty }}\right)=\log {\left(\frac{{N+N}_1}{{N+N}_2}\right)}^b$